Title Topic 2 Part 2 T.pdf ✅

7e. [7 marks] (i) On a different diagram, sketch the graph of where . (ii) Find all solutions of the equation . y = f(|x|) x ∈ D f(|x|) = −1 4 8a. [9 marks] (i) Express each of the complex numbers and in modulus-argument form. (ii) Hence show that the points in the complex plane representing , and form the vertices of an equilateral triangle. (iii) Show that where . z = + i, = − + i 1 3 – √ z2 3 – √ z = −2i 3 z1 z2 z3 z + = 2 3n 1 z 3n 2 z 3n 3 n ∈ N 8b. [9 marks] (i) State the solutions of the equation for , giving them in modulus-argument form. (ii) If w is the solution to with least positive argument, determine the argument of 1 + w. Express your answer in terms of . (iii) Show that is a factor of the polynomial . State the two other quadratic factors with real coefficients. z = 1 7 z ∈ C z = 1 7 π z − 2zcos( ) + 1 2 2π 7 z − 1 7 9a. [4 marks] The function f is defined as . (i) Sketch the graph of , clearly indicating any asymptotes and axes intercepts. (ii) Write down the equations of any asymptotes and the coordinates of any axes intercepts. f(x) = −3 + , x ≠ 2 1 x−2 y = f(x) 9b. [4 marks] Find the inverse function f , stating its domain. −1